The basic idea here is that, for each possible arrangement, if EVERYONE moves 1 seat to the right, we have the same configuration. Likewise, if EVERYONE moves 2 seats to the right, we have the same configuration. Likewise, if EVERYONE moves 3 seats to the right, we have the same configuration. ...Likewise, if EVERYONE moves 7 seats to the right, we have the same configuration. So, one seating arrangement has 8 equivalent arrangements

At this point, let's NUMBER the 8 chairs as follows: #1, #2, #3, ..... #7 and #8We'll call the six people A, B, C, D, E and F

Now seat each person. We can place person A in one of 8 chairsAfter that, we can place person B in one of the 7 remaining chairsAfter that, we can place person C in one of the 6 remaining chairsAfter that, we can place person D in one of the 5 remaining chairsAfter that, we can place person E in one of the 4 remaining chairsAfter that, we can place person F in one of the 3 remaining chairs

So, the number of arrangements = (8)(7)(6)(5)(4)(3)

HOWEVER, we're not quite done. We have counted each equivalent seating 8 times So, to account for this, we must divide (8)(7)(6)(5)(4)(3) by 8 to get: (8)(7)(6)(5)(4)(3)/8 = (7)(6)(5)(4)(3) = 2520